GTFormer: A Syntax-Free Graph Network Alternative to Transformers for 8192$\times$ Length Extrapolation in Linear Time

Elisabeth Fink

cs.LGOct 27, 2026

GTFormer: A Syntax-Free Graph Network Alternative to Transformers for 8192 $\times$ Length Extrapolation in Linear Time

Authors: Elisabeth Fink

Organizations: Middlesex University, Department of Computer Science The Burroughs, Hendon, London NW4 4BT, UK.

Abstract

Self-attention mechanisms have established the Transformer as the dominant backbone across natural language processing, source code intelligence, and automated theorem proving. However, all-to-all pairwise token comparison enforces a quadratic $\mathcal{O}(N^2)$ compute and memory barrier alongside severe softmax attention dilution as sequence length $N$ scales beyond the training horizon. Inspired by recent advances in algebraic graph learning (WPNet), this work introduces GTFormer, a syntax-free hierarchical Graph Neural Network (GNN) that replaces flat self-attention for general long-context sequence modeling. GTFormer organizes raw token streams into a bounded-degree hierarchy combining a balanced binary reduction tree ( $\lceil \log_2 N \rceil$ depth), horizontal boundary-bridging shift edges, random expander shortcuts, multi-channel convex highway gating, and a top-down broadcast pass. Across eight long-context code, log, and multi-hop retrieval benchmarks trained exclusively on sequences of length $N \le 512$ , GTFormer extrapolates zero-shot to $N = 4{,}194{,}304$ ( $8192\times$ ) on a single commodity GPU in linear $\mathcal{O}(N)$ memory, maintaining near-perfect accuracy where standard and RoPE Transformers suffer from out-of-distribution attention collapse and out-of-memory exhaustion.

Figures & tables

Panel of Figure 1 — Figure 1: Structural comparison of information routing over a sequence of length $N=8$ containing an odd-split key-value binding $[K_{r},V_{v}]$ at indices $(3,4)$ and a pointer $[P_{p},K_{r}]$ at indices $(7,8)$ . (a) GTFormer: Local 1-hop horizontal shift edges (orange) bind adjacent tokens across odd binary boundaries before hierarchical reduction. At each tree level, shared-salience convex highway gates suppress filler nodes (dashed gray) and route active variable and pointer channels (solid blue) to the root in $\log_{2}N$ steps and $O(N)$ memory. (b) Flat Transformer: All-to-all $O(N^{2})$ self-attention connects every filler token to every other token, causing severe softmax attention dilution on out-of-distribution lengths and quadratic VRAM exhaustion.

Task Name	Input Token Sequence ( $N=16$ )	Event Progression / Semantics	Target Class
override_qa	[42, 203, 118, 207, 12, 201, 88, 206, 91, 155, 202, 33, 200, 77, 94, 18]	$r_{0}\leftarrow 3\to r_{1}\leftarrow 3\to r_{0}\leftarrow 1\to r_{1}\leftarrow 2\to r_{2}\leftarrow 1$ . Final state: $[1,2,1]$	25
unaligned_kv	[42, 118, 12, 200 , 205 , 88, 201 , 203 , 91, 155, 202 , 206 , 33, 200 , 204 , 77]	Odd-boundary pairs: $[K_{0},V_{2}]\to[K_{1},V_{0}]\to[K_{2},V_{3}]\to[K_{0},V_{1}]$ . Final state: $[1,0,3]$	19
pointer_hop_triple	[14, 213 , 83, 212 , 90, 214 , 111, 200 , 211 , 49, 201 , 208 , 170, 202 , 210 , 88]	$V_{0}\leftarrow 3$ , $V_{1}\leftarrow 0$ , $V_{2}\leftarrow 2$ ; Dereference $\text{PTR}_{0}\to V_{1}$ , $\text{PTR}_{1}\to V_{0}$ , $\text{PTR}_{2}\to V_{2}$ $\implies$ final values = [0, 3, 2]	14
intrusion_fsm	[81, 203 , 45, 207 , 19, 250 , 99, 110, 202 , 130, 14, 66, 92, 140, 50, 12]	$r_{0}\leftarrow 3,r_{1}\leftarrow 3\to\text{{RESET}}(250)\implies[0,0,0]\to r_{0}\leftarrow 2$ Final state: $[2,0,0]$	32
code_scope_shadow	[ 202 , 41, 260 , 12, 203 , 89, 261 , 73, 99, 102, 18, 45, 160, 11, 82, 39]	Global $r_{0}\leftarrow 2\to\text{{ENTER}}(260)\to\text{Local }r_{0}\leftarrow 3\to\text{{EXIT}}(261)\implies$ revert to 2 Final state: [2,0,0]	32
multi_needle_rag	[18, 201 , 207 , 44, 210 , 92, 200 , 206 , 11, 145, 202 , 209 , 67, 83, 104, 5]	Query $Q_{0}(210)\implies\text{retrieve }(E_{0},E_{1},E_{2})$ ; Bindings: $E_{1}\leftarrow 1,E_{0}\leftarrow 0,E_{2}\leftarrow 3$ Retrieved slots: $[0,1,3]$	7

Table 1: Representative token input sequences, event streams, and target output states across the eight benchmark tasks for sequence length

N=16

(vocabulary size

V=320

). Filler tokens

t\in[0,199]

represent background noise; tokens

t\geq 200

carry structured operational semantics.

Panel of Figure 2 — Figure 2: Architecture of the syntax-free GTFormer topology shown for $N=8$ ( $D=3$ ). At Level $d=0$ , an unaligned two-token phrase $[\textit{KEY},\textit{VAL}]$ at odd indices $(v_{1}^{(0)},v_{2}^{(0)})$ straddles the boundary between subtrees $v_{0}^{(1)}$ and $v_{1}^{(1)}$ , but is bound locally via the horizontal shift edge $\mathcal{E}_{\text{shift}}$ ( $v_{2}^{(0)}\to v_{1}^{(0)}$ ). Bottom-up tree edges $\mathcal{E}_{\text{tree}}$ and horizontal expander shortcuts $\mathcal{E}_{\text{exp}}$ compress sequence state in $\log_{2}N$ steps, while top-down broadcast edges $\mathcal{E}_{\text{down}}$ resolve remote pointer queries ( PTR ).

Model Variant	Topology	Local Shift	Expander	Convex Gate	Top-Down	Primary Role / Ablation Target
		( use_local_shift )	( use_expander )	( use_convex_gate )	( use_top_down )
GTFormer_Bidirectional	Hierarchical	✓	✓	✓	✓	Full proposed architecture
GTFormer_BottomUp	Hierarchical	✓	✓	✓	✗	Feed-forward root readout only
GTFormer_NoExpander	Hierarchical	✓	✗	✓	✓	Ablates horizontal peer shortcuts ( $\mathcal{E}_{\text{exp}}$ )
Pure_Binary_Tree	Hierarchical	✗	✗	✓	✓	No horizontal edges; tests odd-index splitting
Unbounded_Tree_MLP	Hierarchical	✓	✓	✗	✓	Unconstrained MLP merge; tests depth drift

Table 2: Architectural comparison of evaluated model variants and ablation configurations.

Architecture	Time	Memory	Graph	Max	Odd-Split	2-Hop Ptr
			Diam.	Fan-In	Safe	Safe
Flat Transformer (Sin / RoPE)	$\mathcal{O}(N^{2})$	$\mathcal{O}(N^{2})$	$1$	$N$	Yes	Yes (ID)
Pure Binary Tree-GNN	$\mathcal{O}(N)$	$\mathcal{O}(N)$	$2\log N$	$2$	No	No
Unbounded Tree-MLP	$\mathcal{O}(N)$	$\mathcal{O}(N)$	$2\log N$	$3$	Yes	No
GraphTree (Bottom-Up)	$\mathcal{O}(N)$	$\mathcal{O}(N)$	$\leq 2\log N$	$4$	Yes	Partial
GraphTree (Bidirectional)	$\mathbf{\mathcal{O}(N)}$	$\mathbf{\mathcal{O}(N)}$	$\mathbf{\leq 2\log N}$	$\mathbf{4}$	Yes	Yes ( $1024\times$ )

Table 3: Theoretical complexity and structural comparison across sequence length

N

. Bounded fan-in (

\Delta_{\text{in}}\leq 4

) and convex highway gating enable scalable linear extrapolation to

N=4{,}194{,}304

without attention dilution.

Figure 3: Average performance on all tests in zero-shot extrapolation of all architectures.

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$	$N=4096$	$N=16384$
GraphTree (Bidirectional: Up + Down)	$70.8\%$	$72.0\%$	$72.1\%$	$72.2\%$	$71.8\%$	$71.2\%$
GraphTree (Bottom-Up + Shortcuts)	$97.3\%$	$97.3\%$	$97.3\%$	$97.3\%$	$97.3\%$	$95.5\%$
GraphTree (Local Shift, No Expander)	$97.8\%$	$97.9\%$	$98.0\%$	$97.8\%$	$97.9\%$	$97.7\%$
Pure Binary Tree-GNN (No Shortcuts)	$86.7\%$	$86.5\%$	$86.9\%$	$86.9\%$	$85.9\%$	$83.3\%$
Unbounded Tree-GNN (No Convex Gate)	$3.0\%$	$3.1\%$	$3.5\%$	$3.1\%$	$3.1\%$	$2.8\%$
Flat Transformer (Sinusoidal)	$59.5\%$	$54.3\%$	$53.9\%$	$32.4\%$	$16.0\%$	OOM

Table 4: Aggregate summary of results over all eight tasks (OOM=Out-Of-Memory).

Architecture	$N=64$	$N=256$	$N=512$	$N=1024$	$N=4096$	$N=16384$
GraphTree (Local Shift, No Expander)	31 MB	64 MB	108 MB	196 MB	373 MB	725 MB
GraphTree (Bottom-Up + Shortcuts)	32 MB	65 MB	109 MB	197 MB	373 MB	726 MB
GraphTree (Bidirectional: Up + Down)	34 MB	66 MB	111 MB	199 MB	375 MB	728 MB
Pure Binary Tree-GNN	24 MB	36 MB	54 MB	88 MB	156 MB	292 MB
Unbounded Tree-GNN	32 MB	64 MB	109 MB	197 MB	373 MB	726 MB
Flat Transformer (Sinusoidal)	27 MB	45 MB	69 MB	117 MB	213 MB	OOM

Table 5: Memory usage per model and evaluation lenght.

Architecture	$N=64$	$N=256$	$N=512$	$N=1024$	$N=4096$	$N=16384$
GraphTree (Local Shift, No Expander)	0.17 ms	0.23 ms	0.29 ms	0.38 ms	1.12 ms	3.65 ms
GraphTree (Bottom-Up + Shortcuts)	0.24 ms	0.34 ms	0.40 ms	0.51 ms	1.57 ms	5.38 ms
GraphTree (Bidirectional: Up + Down)	0.34 ms	0.42 ms	0.49 ms	0.60 ms	1.69 ms	5.57 ms
Pure Binary Tree-GNN	0.16 ms	0.19 ms	0.21 ms	0.30 ms	0.75 ms	2.33 ms
Unbounded Tree-GNN	0.12 ms	0.17 ms	0.21 ms	0.29 ms	0.89 ms	2.79 ms
Flat Transformer (Sinusoidal)	0.13 ms	0.12 ms	0.17 ms	0.36 ms	2.10 ms	OOM

Table 6: Average training times of all models across the eight tasks.

Figure 4: Performance of the architecture variations on the eight defined tasks.

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.5\pm 0.8\%$	$1.6\pm 0.9\%$	$1.6\pm 0.6\%$	$1.1\pm 0.8\%$	$1.4\pm 1.0\%$	$1.2\pm 1.2\%$
Flat Transformer (Sinusoidal)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$16.0\pm 4.4\%$	$6.1\pm 3.8\%$	OOM

Appendix

Table A1: Zero-shot length extrapolation accuracy on task override_qa (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$	$98.8\pm 2.5\%$	$97.5\pm 3.1\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.9\pm 1.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$3.8\pm 3.1\%$	$3.8\pm 5.0\%$	$0.0\pm 0.0\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A2: Zero-shot length extrapolation accuracy on task override_qa (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$99.7\pm 0.6\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$98.9\pm 1.1\%$	$98.0\pm 1.1\%$	$99.3\pm 0.8\%$	$98.7\pm 0.9\%$	$96.2\pm 4.3\%$	$91.2\pm 9.6\%$
Unbounded Tree-GNN (No Convex Gate)	$0.8\pm 0.6\%$	$1.0\pm 0.7\%$	$1.8\pm 0.8\%$	$1.7\pm 0.6\%$	$1.2\pm 0.4\%$	$0.6\pm 0.8\%$
Flat Transformer (Sinusoidal)	$19.8\pm 3.8\%$	$7.8\pm 2.5\%$	$4.4\pm 0.7\%$	$2.3\pm 0.2\%$	$1.4\pm 0.9\%$	OOM

Appendix

Table A3: Zero-shot length extrapolation accuracy on task unaligned_kv (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Bottom-Up + Shortcuts)	$96.9\pm 6.2\%$	$95.0\pm 10.0\%$	$88.8\pm 22.5\%$	$82.5\pm 35.0\%$	$81.2\pm 34.5\%$	$77.5\pm 39.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$86.9\pm 14.3\%$	$75.0\pm 23.1\%$	$72.5\pm 19.2\%$	$56.2\pm 34.0\%$	$58.8\pm 31.8\%$	$60.0\pm 30.0\%$
Unbounded Tree-GNN (No Convex Gate)	$0.6\pm 1.2\%$	$1.2\pm 2.5\%$	$0.0\pm 0.0\%$	$0.0\pm 0.0\%$	$2.5\pm 3.1\%$	$3.8\pm 3.1\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A4: Zero-shot length extrapolation accuracy on task unaligned_kv (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$8.1\pm 1.5\%$	$10.4\pm 2.4\%$	$10.7\pm 1.0\%$	$12.0\pm 2.6\%$	$11.6\pm 1.8\%$	$8.4\pm 1.6\%$
GraphTree (Bottom-Up + Shortcuts)	$88.4\pm 23.1\%$	$88.0\pm 24.0\%$	$88.1\pm 23.8\%$	$88.0\pm 24.0\%$	$89.2\pm 20.8\%$	$75.9\pm 35.2\%$
GraphTree (Local Shift, No Expander)	$92.5\pm 15.0\%$	$93.5\pm 12.9\%$	$93.8\pm 12.3\%$	$92.9\pm 14.2\%$	$93.6\pm 12.8\%$	$92.2\pm 15.6\%$
Pure Binary Tree-GNN (No Shortcuts)	$9.0\pm 2.1\%$	$10.8\pm 2.3\%$	$10.8\pm 1.3\%$	$10.8\pm 1.7\%$	$10.5\pm 1.1\%$	$11.6\pm 2.3\%$
Unbounded Tree-GNN (No Convex Gate)	$1.5\pm 0.8\%$	$1.2\pm 0.7\%$	$2.2\pm 1.0\%$	$1.7\pm 0.6\%$	$1.9\pm 0.8\%$	$1.6\pm 1.0\%$
Flat Transformer (Sinusoidal)	$8.7\pm 1.8\%$	$5.5\pm 2.0\%$	$4.3\pm 1.3\%$	$3.6\pm 0.7\%$	$2.3\pm 0.9\%$	OOM

Appendix

Table A5: Zero-shot length extrapolation accuracy on task pointer_hop (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$3.8\pm 3.1\%$	$7.5\pm 7.3\%$	$0.0\pm 0.0\%$	$2.5\pm 3.1\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$
GraphTree (Bottom-Up + Shortcuts)	$61.2\pm 46.2\%$	$61.2\pm 45.1\%$	$60.0\pm 46.5\%$	$60.0\pm 44.1\%$	$57.5\pm 47.2\%$	$52.5\pm 45.0\%$
GraphTree (Local Shift, No Expander)	$93.1\pm 13.8\%$	$93.8\pm 12.5\%$	$92.5\pm 15.0\%$	$90.0\pm 20.0\%$	$95.0\pm 10.0\%$	$88.8\pm 19.5\%$
Pure Binary Tree-GNN (No Shortcuts)	$13.8\pm 7.3\%$	$11.2\pm 4.7\%$	$11.2\pm 13.3\%$	$8.8\pm 8.5\%$	$8.8\pm 3.1\%$	$12.5\pm 6.8\%$
Unbounded Tree-GNN (No Convex Gate)	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$2.5\pm 3.1\%$	$1.2\pm 2.5\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A6: Zero-shot length extrapolation accuracy on task pointer_hop (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.7\pm 0.4\%$	$2.1\pm 0.9\%$	$1.8\pm 1.2\%$	$1.6\pm 0.9\%$	$2.3\pm 1.1\%$	$2.8\pm 1.8\%$
Flat Transformer (Sinusoidal)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$30.8\pm 7.1\%$	$17.7\pm 5.1\%$	OOM

Appendix

Table A7: Zero-shot length extrapolation accuracy on task intrusion_fsm (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.2\pm 1.5\%$	$5.0\pm 4.7\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$0.0\pm 0.0\%$	$1.2\pm 2.5\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A8: Zero-shot length extrapolation accuracy on task intrusion_fsm (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$84.9\pm 30.2\%$	$85.8\pm 28.3\%$	$85.5\pm 29.0\%$	$87.0\pm 26.0\%$	$85.3\pm 29.4\%$	$85.6\pm 28.8\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.8\pm 0.5\%$	$1.2\pm 0.5\%$	$1.8\pm 0.5\%$	$1.5\pm 0.8\%$	$0.6\pm 0.6\%$	$2.5\pm 1.6\%$
Flat Transformer (Sinusoidal)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$30.4\pm 15.9\%$	$13.9\pm 5.4\%$	OOM

Appendix

Table A9: Zero-shot length extrapolation accuracy on task code_scope_shadow (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$87.5\pm 23.5\%$	$85.0\pm 30.0\%$	$85.0\pm 30.0\%$	$81.2\pm 34.5\%$	$87.5\pm 25.0\%$	$83.8\pm 29.5\%$
GraphTree (Bottom-Up + Shortcuts)	$98.8\pm 2.5\%$	$100.0\pm 0.0\%$	$95.0\pm 7.3\%$	$88.8\pm 17.0\%$	$91.2\pm 9.3\%$	$81.2\pm 15.8\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$	$98.8\pm 2.5\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$1.2\pm 1.5\%$	$1.2\pm 2.5\%$	$2.5\pm 3.1\%$	$2.5\pm 3.1\%$	$0.0\pm 0.0\%$	$2.5\pm 3.1\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A10: Zero-shot length extrapolation accuracy on task code_scope_shadow (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$8.2\pm 1.9\%$	$10.7\pm 2.7\%$	$10.9\pm 0.9\%$	$11.3\pm 2.1\%$	$9.1\pm 0.9\%$	$12.2\pm 2.3\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$9.2\pm 2.8\%$	$12.2\pm 3.9\%$	$10.8\pm 2.3\%$	$12.2\pm 1.7\%$	$11.4\pm 2.0\%$	$11.2\pm 1.5\%$
Unbounded Tree-GNN (No Convex Gate)	$1.5\pm 0.8\%$	$1.2\pm 0.7\%$	$2.2\pm 1.0\%$	$1.7\pm 0.6\%$	$1.9\pm 0.8\%$	$1.6\pm 1.0\%$
Flat Transformer (Sinusoidal)	$9.1\pm 1.1\%$	$5.0\pm 2.0\%$	$4.8\pm 0.6\%$	$2.9\pm 0.7\%$	$1.9\pm 0.6\%$	OOM

Appendix

Table A11: Zero-shot length extrapolation accuracy on task multi_needle_rag (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$11.9\pm 4.6\%$	$13.8\pm 6.1\%$	$11.2\pm 13.3\%$	$6.2\pm 6.8\%$	$8.8\pm 6.4\%$	$8.8\pm 7.5\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$12.5\pm 7.1\%$	$12.5\pm 5.6\%$	$16.2\pm 12.9\%$	$8.8\pm 6.4\%$	$13.8\pm 4.7\%$	$16.2\pm 7.5\%$
Unbounded Tree-GNN (No Convex Gate)	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$2.5\pm 3.1\%$	$1.2\pm 2.5\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A12: Zero-shot length extrapolation accuracy on task multi_needle_rag (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$96.7\pm 6.7\%$	$96.9\pm 6.2\%$	$96.7\pm 6.7\%$	$96.6\pm 6.9\%$	$97.0\pm 5.9\%$	$96.9\pm 6.2\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$11.9\pm 1.8\%$	$14.0\pm 1.8\%$	$15.3\pm 2.1\%$	$10.4\pm 1.8\%$	$11.7\pm 2.6\%$	$8.1\pm 3.8\%$
Flat Transformer (Sinusoidal)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$99.0\pm 1.3\%$	$51.1\pm 13.0\%$	OOM

Appendix

Table A13: Zero-shot length extrapolation accuracy on task xml_bracket_check (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$96.9\pm 6.2\%$	$97.5\pm 5.0\%$	$98.8\pm 2.5\%$	$95.0\pm 10.0\%$	$95.0\pm 10.0\%$	$100.0\pm 0.0\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$98.8\pm 2.5\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Unbounded Tree-GNN (No Convex Gate)	$11.2\pm 7.5\%$	$17.5\pm 7.3\%$	$13.8\pm 10.0\%$	$10.0\pm 5.0\%$	$11.2\pm 4.7\%$	$17.5\pm 6.1\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A14: Zero-shot length extrapolation accuracy on task xml_bracket_check (Part 2).

Architecture	$N=64$ (ID)	$N=256$ (ID)	$N=512$ (ID)	$N=1024$ (OOD)	$N=4096$ (OOD)	$N=16384$ (OOD)
GraphTree (Bidirectional: Up + Down)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$99.4\pm 1.2\%$
GraphTree (Bottom-Up + Shortcuts)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$
Pure Binary Tree-GNN (No Shortcuts)	$98.7\pm 1.1\%$	$98.0\pm 1.0\%$	$99.1\pm 1.0\%$	$99.0\pm 1.1\%$	$97.7\pm 2.6\%$	$91.2\pm 10.9\%$
Unbounded Tree-GNN (No Convex Gate)	$3.0\pm 3.8\%$	$2.9\pm 2.3\%$	$2.4\pm 1.1\%$	$2.9\pm 2.3\%$	$2.8\pm 1.5\%$	$1.9\pm 2.5\%$
Flat Transformer (Sinusoidal)	$17.9\pm 2.8\%$	$3.5\pm 1.0\%$	$3.6\pm 1.7\%$	$1.9\pm 0.6\%$	$1.4\pm 0.6\%$	OOM

Appendix

Table A15: Zero-shot length extrapolation accuracy on task adversarial_decoys (Part 1).

Architecture	$N=65536$	$N=131072$	$N=262144$	$N=524288$	$N=1048576$	$N=2097152$
GraphTree (Bidirectional: Up + Down)	$92.5\pm 15.0\%$	$83.8\pm 32.5\%$	$82.5\pm 35.0\%$	$81.2\pm 37.5\%$	$81.2\pm 37.5\%$	$80.0\pm 40.0\%$
GraphTree (Bottom-Up + Shortcuts)	$99.4\pm 1.2\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$97.5\pm 3.1\%$	$95.0\pm 7.3\%$	$96.2\pm 5.0\%$
GraphTree (Local Shift, No Expander)	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$100.0\pm 0.0\%$	$97.5\pm 5.0\%$	$98.8\pm 2.5\%$
Pure Binary Tree-GNN (No Shortcuts)	$86.2\pm 13.2\%$	$86.2\pm 18.7\%$	$75.0\pm 23.1\%$	$81.2\pm 17.2\%$	$70.0\pm 18.3\%$	$66.2\pm 25.2\%$
Unbounded Tree-GNN (No Convex Gate)	$1.9\pm 3.8\%$	$2.5\pm 3.1\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$1.2\pm 2.5\%$	$2.5\pm 3.1\%$
Flat Transformer (Sinusoidal)	OOM	OOM	OOM	OOM	OOM	OOM

Appendix

Table A16: Zero-shot length extrapolation accuracy on task adversarial_decoys (Part 2).

Long-Context Modeling

Long-context modeling studies how AI systems process, retrieve, and reason over sequences that exceed ordinary context windows.

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Graph Memory Transformer (GMT)
Apr 26, 2026Nicola Zanarini, Niccolò Ferrari, Evelina LammaMemory-Augmented Neural Networks Transformer FFNs
Bonfiglioli Engineering s.r.l. · Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy · NAIS s.r.l., Via Maria Callas 4, 40131 Bologna, Italy
Teaching LLMs to See Graphs: Unifying Text and Structural Reasoning
May 11, 2026Dario VajdaLLM Reasoning with Graphs Text-Attributed Graph Learning
Faculty of Computer and Information Science University of Ljubljana
LongAttnComp: Cross-Family Context Compression for Long-Context Reasoning
May 31, 2026Mengmeng Ji, Ravi Shanker Raju, Jonathan Lingjie Li +1LLM Compression LLM Fine-Tuning
SambaNova Systems, Inc. San Jose, CA, USA

Apr 26, 2026J/K move · Enter open · S save

Graph Memory Transformer (GMT)

Nicola Zanarini, Niccolò Ferrari, Evelina Lamma

Bonfiglioli Engineering s.r.l. · Department of Engineering, University of Ferrara, Via Saragat 1, 44122 Ferrara, Italy · NAIS s.r.l., Via Maria Callas 4, 40131 Bologna, Italy

Memory-Augmented Neural Networks Transformer FFNs Graph Neural Networks Memory-Augmented Language Models Transformer Decoder-Only Language Models

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We investigate whether an explicit learned memory graph can replace the Feed-Forward Network (FFN) sublayer in a decoder-only transformer while preserving the surrounding autoregressive architecture. In the proposed graph Memory Transformer (GMT), a memory cell routes token representations over a learned bank of centroids connected by a learned directed transition matrix, while causal self-attention remains unchanged. In the base v7 instantiation, each of 16 transformer blocks contains 128 centroids and a 128 x 128 edge matrix. Each cell uses gravitational source routing and token-conditioned target selection to return a gated displacement from the estimated source memory state toward the target memory state, rather than a retrieved value. The resulting decoder-only language model has 82.2M trainable parameters and no dense FFN sublayers; the evaluated dense GPT-style baseline has 103.0M. It trains stably and exposes centroid usage, transition structure, and source-to-target movement for direct inspection in the forward computation. It trails the larger baseline in validation loss and perplexity (3.5995/36.58 vs. 3.2903/26.85), while showing close zero-shot benchmark behavior under the evaluated setting. These results support the viability and structural interpretability of replacing dense within-token transformation with graph-mediated memory navigation, without claiming state-of-the-art performance. Broader scaling, optimized kernels, and more extensive benchmark evaluation remain for future work.

Abstract

Long-Context Modeling

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